JOURNAL 



OF THE 



WASHINGTON ACADEMY OF SCIENCES 



Vol. Ill MAY 4, 1913 No. 9 



VITAL STATISTICS.^ — A natural population norm^ I. Alfked 

 J. LoTKA. Communicated by G. K. Burgess. 



Birthrate and deathrate are in general functions of the age- 

 distribution in a given population. Hence, for purposes of com- 

 parison, it is customary to "correct," the "crude" death rates 

 to correspond to some arbitrarily chosen "standard population." 



The age distribution itself is not, however, purely fortuitous, 

 but tends to approach a certain "stable" type, as has been shown 

 by the writer elsewhere. ^ 



Instead, therefore, of studying conditions in an arbitrary stand- 

 ard population, it seems worth while to study the characteristics 

 of a "natural population norm," in which the stable age-distri- 

 bution is actually established. This is the purpose of the present 

 paper. At the same time we shall compare the results obtained 

 for such an "ideal" population norm, with figures actually 

 observed in a case which approaches very nearly the calculated 

 "normal" conditions. 



I. Birthrate, deathrate and age-distribution in life. As the 

 basis of our present discussion we shall use the formulae developed 

 on a previous occasion, which are as follows. 



1 Paper read before the Philosophical Society of Washington on February 1, 

 1913. 



2 Am. Jl. Sc. 24: 199, 375. 1907. Science 26: 21. 1907. Phil. Mag., p. 435. 

 April 1911. Compare also Bristowe, St. Thomas's Hospital Report, 1876, as 

 quoted in A. Newsholme, Vital Statistics, p. 295. 1899. 



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